The value measured in the amorphous structure with the same chemical
composition is often considered as a lower bound for the thermal
conductivity of any material: the heat carriers are strongly scattered
by disorder, and their lifetimes reach the minimum time scale of thermal
vibrations. An appropriate design at the nano-scale, however, may allow
one to reduce the thermal conductivity even below the amorphous limit.
In the present contribution, using molecular-dynamics simulation and the
Green-Kubo formulation, we study systematically the thermal conductivity
of layered phononic materials (superlattices), by tuning different
parameters that can characterize such structures. We have discovered
that the key to reach a lower-than-amorphous thermal conductivity is to
block almost completely the propagation of the heat carriers, the
superlattice phonons. We demonstrate that a large mass difference in the
two intercalated layers, or weakened interactions across the interface
between layers result in materials with very low thermal conductivity,
below the values of the corresponding amorphous counterparts.